1) What is polylang for responsive?
2) it should be there. Do you already have a second language? And a menu?
3) you can. Using CSS, but you should add larger icons to have them display nicely. I could get back to you on the exact place to put the flags. I think it is in wp-content/polylang (a new folder which you should create), but not sure, maybe someone can confirm (sorry, no acces to my sources at this moment).
I prefer using languages codes instead (en, fr, ...). This is less confusing since English, Dutch, French, ...are spoken in several countries. You can achieve this easily by adding them as icons the same way.
4) yes, using CSS. If you're not familiar with it you should check out some online sources on it (like W3schools. Or you could post a link to your website for more detailed suggestions.